Shape

402 Notes to pp. 305–306
the world into meaningful units] is the essence of intelligence and the hard part of the problems
being solved. Under the current scheme the abstraction is done by the researchers leaving little for
the AI programs to do but search. A truly intelligent program would study the photograph, perform
the abstraction and solve the problem.’’ Is it any wonder that Brooks gives up on the current
scheme and search, when parts of shapes—what’s in the photograph—are resolved only in some
sort of precalculating? ‘‘[This abstraction] is the essence of intelligence’’ and of calculating with
shapes and rules, too. (Visual experience—in fact, photography—was also decisive for Susanne
Langer when she abandoned vocabulary and syntax for presentational forms of symbolism.)
Brooks appeals to perception and action (seeing and doing) to make autonomous mobile agents
or ‘‘Creatures.’’ They segment the world and change it. The analogy goes like this
Creatures : world(s) < rules : shape(s)
although the idea was clear to C. S. Peirce (page 55) 125 years ago. He thought Creatures were
creatures of habit. Yet something is amiss. Creatures act like cellular automata in that ‘‘there
emerges, [only] in the eye of an [outside] observer, a coherent pattern of behavior.’’ Embedding
and transformations, and the ensuing ambiguity, aren’t part of perception for Creatures. Intelligence
caps a recursive ascent, but what kind of intelligence is unaware of itself and what it does?
It’s pretty much the same drawing the three lines on page 2 and not seeing the triangle, or rotating
three triangles in the series on page 296 and not trying two. Why should perception stop?
Then everything adds up without making anything new. Action is senseless when there’s no way
to see what’s going on. (In fact, this is the same kind of problem I had earlier in note 9 with music
and Bamberger’s units of perception and units of work. The distinction is a hobbling artifact of
representation and another reason to try something new. Units fail for perception whether seeing
or hearing, and when there’s creative work to do. But this is never a problem with shapes and
rules—then one ‘‘size’’ fits all.)
26. A. N. Whitehead, Process and Reality (New York: Free Press, 1978), 294–297.
27. H. Leonard and N. Goodman, ‘‘The Calculus of Individuals and Its Uses,’’ Journal of Symbolic
Logic 5 (1940): 45. See also N. Goodman, The Structure of Appearance, 46–56.
28. A. Tarski, ‘‘Foundations of the Geometry of Solids,’’ in Logic, Semantics, Metamathematics,
trans. J. H. Woodger (Indianapolis: Hackett, 1983), 24–29.
29. P. Simons, Parts: A Study in Ontology (Oxford: Clarendon Press, 1987).
30. N. Goodman and W. V. Quine, ‘‘Steps toward a Constructive Nominalism,’’ in Problems and
Projects, ed. N. Goodman (Indianapolis: Bobbs-Merrill, 1972), 173–198.
31. A. Tarski, ‘‘On the Foundations of Boolean Algebra,’’ in Logic, Semantics, Metamathematics,
333, fn. 1.
32. A. A. G. Requicha, ‘‘Representations of Rigid Solids: Theory, Methods, and Systems,’’ ACM
Computer Surveys 12 (1980): 437–464.
33. M. H. Stone, ‘‘The Theory of Representations for Boolean Algebras,’’ Transactions of the American
Mathematical Society 40 (1936): 37–111.
34. Earl, ‘‘Shape Boundaries.’’ For a scattered but more detailed account of the same material, see
H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, 3rd ed. (Warsaw: Panstwowe
Wydawnictwo Naukowe, 1970).